Finite Size Effects on Spin Glass Dynamics

Abstract

The recent identification of a time and temperature dependent spin glass correlation length, $ξ({t_w},T)$, has consequences for samples of finite size. Qualitative arguments are given on this basis for departures from t/{t_w} scaling for the time decay of the thermoremanent magnetization, {M_{TRM}}(t,{t_w},T), where t is the measurement time after a ``waiting time'' t_w, and for the imaginary part of the ac susceptibility, ${χ^{{\prime}{\prime}}}(ω,t)$. Consistency is obtained for a more rapid decay of $M_{TRM}(t,{t_w},T)$ with increasing t_w when plotted as a function of t/{t_w}, for the deviation of the characteristic time for {M_{TRM}}(t,{t_w},T) from a linear dependence upon H^2 at larger values of H, and for the deviation of the decay of ${χ^{{\prime}{\prime}}}(ω,t)$ from $ωt$ scaling upon a change in magnetic field at large values of $ωt$. These departures from scaling can, in principle, be used to extract the particle size distribution for a given spin glass sample.